Jane Street Data Scientist Interview Guide

Explain that averages of samples tend toward normal distribution regardless of population distribution. Use simple analogy (coin flips, heights). Connect to confidence intervals and hypothesis testing. Show ability to communicate technical concepts simply.

Set up hypothesis test (H0: p=0.5), calculate z-score or use binomial test, determine p-value, choose significance level. Discuss assumptions, statistical vs practical significance, and confidence intervals. Show rigorous statistical thinking.

Correlation measures association, causation implies one causes the other. Discuss confounding variables, randomized controlled trials, instrumental variables, diff-in-diff, and causal inference frameworks. Give real examples of spurious correlations.

P-hacking is manipulating data or analysis to achieve significant p-values. Discuss pre-registering hypotheses, Bonferroni correction for multiple comparisons, separating exploratory vs confirmatory analysis, and cross-validation. Show ethical awareness.

P(A|B) = P(B|A) * P(A) / P(B). Use medical testing or spam filtering example. Discuss prior probability, likelihood, posterior probability, and how it updates beliefs with new evidence. Show understanding of probabilistic thinking.

Define success metric, calculate required sample size using power analysis (typically 80% power, 5% significance), determine test duration, discuss randomization strategy, and statistical test choice. Cover practical issues like network effects and seasonality.

Discuss linearity, independence, homoscedasticity, normality of errors. Use residual plots, Q-Q plots, variance inflation factor (VIF) for multicollinearity, Durbin-Watson for autocorrelation. Explain what to do when assumptions are violated.

High bias = underfitting (too simple), high variance = overfitting (too complex). Discuss learning curves, cross-validation, regularization techniques (L1/L2), and finding the sweet spot. Use visual analogy of fitting data points.

Decision tree - interpretability needed, simple baseline. Random forest - reduce variance, handle non-linearity, less tuning. Gradient boosting - best performance, handles complex patterns, more tuning required. Discuss computational cost and overfitting risks.

Discuss resampling (SMOTE, undersampling), class weights, different metrics (precision/recall, F1, ROC-AUC), threshold adjustment, and anomaly detection approaches. Explain when each technique is appropriate and potential pitfalls.

L1 (Lasso) drives some coefficients to zero (feature selection), L2 (Ridge) shrinks all coefficients (prevents overfitting). L1 for sparse solutions, L2 when all features matter. Discuss Elastic Net as combination and computational considerations.

Discuss precision@k, recall@k, MAP (Mean Average Precision), NDCG (Normalized Discounted Cumulative Gain), coverage, diversity, and serendipity. Cover online metrics (CTR, engagement) vs offline metrics. Discuss cold start problem and A/B testing considerations.

Gradient descent minimizes loss by iteratively moving in direction of steepest descent. Batch uses all data (stable but slow), SGD uses single sample (fast but noisy), mini-batch balances both. Discuss learning rate, convergence, and when to use each.

As dimensions increase, data becomes sparse and distance metrics lose meaning. Discuss exponential growth in data needed, distance concentration, and overfitting. Cover dimensionality reduction techniques (PCA, t-SNE, feature selection) and when they help.

Iteratively assigns points to nearest centroid, updates centroids. Limitations - assumes spherical clusters, sensitive to initialization, requires pre-specifying k, sensitive to outliers. Discuss elbow method, silhouette score, and alternatives like DBSCAN or hierarchical clustering.

Discuss regularization (L1/L2, dropout), early stopping, data augmentation, batch normalization, reducing model complexity, and cross-validation. Explain monitoring train vs validation loss curves. Show practical experience with deep learning.

Bagging (Bootstrap Aggregating) trains parallel models on random subsets, reduces variance (Random Forest). Boosting trains sequential models where each corrects previous errors, reduces bias (XGBoost, AdaBoost). Discuss when to use each and computational trade-offs.

Multiple approaches - use DISTINCT with LIMIT/OFFSET, subquery with MAX, or window functions (DENSE_RANK). Discuss handling edge cases (ties, null values, less than 2 salaries). Show understanding of SQL optimization.

Detection methods - IQR, z-score, isolation forest, visual inspection (box plots). Handling - remove (if errors), cap/floor (winsorization), transform (log), or build robust models. Discuss domain knowledge importance and impact on downstream analysis.

INNER (matching records), LEFT/RIGHT (all from one table), FULL OUTER (all from both), CROSS (cartesian product). Give examples with employees and departments. Discuss performance implications and when to denormalize.

Options - deletion (listwise, pairwise), imputation (mean, median, mode, regression, KNN, MICE), modeling missingness explicitly. Discuss MCAR, MAR, MNAR types. Cover impact on bias and variance. Show understanding of domain context.

Normalization scales to [0,1] range (min-max scaling), standardization to mean=0, std=1 (z-score). Use standardization for algorithms assuming normal distribution (linear regression, PCA), normalization for neural networks. Discuss impact of outliers.

Discuss data sources, extraction methods, transformation logic, validation checks, error handling, incremental vs full loads, scheduling (Airflow), monitoring, and scalability (Spark, distributed processing). Cover data quality and lineage tracking.

Discuss creating interaction terms, polynomial features, binning, encoding categorical variables (one-hot, target encoding), datetime features, aggregations, and domain-specific features. Give concrete examples. Show creativity and domain knowledge.

Techniques - target encoding, frequency encoding, embedding layers (neural nets), grouping rare categories, hashing trick. Discuss overfitting risks and when to use each. Cover memory and computational considerations.

Precision = TP/(TP+FP), Recall = TP/(TP+FN), F1 = harmonic mean. Optimize precision when false positives are costly (spam detection), recall when false negatives are costly (disease screening). Discuss ROC-AUC and PR curves.

Consider interpretability, inference time, training time, memory footprint, maintenance cost, robustness to data drift, fairness metrics, and business constraints. Discuss the Occam's razor principle and starting with simpler models.

K-fold (split into k parts), stratified (preserve class distribution), time series (respects temporal order), leave-one-out. Prevents overfitting, provides better performance estimate. Discuss computational cost and when to use each type.

Use visualizations, avoid jargon, focus on business impact, tell stories with data, use analogies, and connect to KPIs. Discuss tailoring message to audience (executives vs product managers). Give specific example of translating technical results.

Use STAR method. Quantify impact (revenue, cost savings, efficiency gains). Discuss how you framed the problem, data sources, analysis approach, insights, recommendations, and follow-up. Show business acumen and impact focus.

Discuss impact vs effort matrix, stakeholder alignment, dependencies, quick wins vs long-term projects, and communication. Show understanding of business priorities and pragmatic decision-making.

Listen to concerns, validate their intuition, check for data quality issues or biases, explain model limitations, consider domain knowledge, and be willing to iterate. Show humility and collaboration skills.

List comprehension creates full list in memory, generators yield one item at a time. Use generators for large datasets or infinite sequences to save memory. Discuss lazy evaluation and performance trade-offs. Give code examples.

Use cProfile or line_profiler to identify bottlenecks, vectorize with NumPy/Pandas, use appropriate data structures (dict vs list), avoid loops with apply/map, consider Cython or multiprocessing. Discuss premature optimization pitfalls.

Shallow copy creates new container but references same objects, deep copy recursively copies everything. Matters for nested structures (lists of lists). Discuss using copy.copy() vs copy.deepcopy() and performance implications.

Features - query characteristics, user history, time/location, ad quality scores. Consider logistic regression baseline, then gradient boosting. Discuss handling cold start, online learning, and calibration. Show understanding of ad ecosystem and billions of queries scale.

Discuss two-stage approach (candidate generation + ranking), features (watch history, engagement signals, video metadata), collaborative filtering, deep learning (two-tower model), and balancing exploration-exploitation. Cover metrics like watch time and diversity.

Define engagement metrics (time spent, interactions, DAU/MAU), design A/B test with proper randomization, consider network effects and spillover, use long-term holdout for delayed effects. Discuss statistical power and heterogeneous treatment effects.

Features - account age, posting patterns, follower/following ratio, engagement rates, profile completeness, behavior anomalies. Use ensemble of supervised (labeled data) and unsupervised (anomaly detection). Discuss precision/recall trade-offs and adversarial ML challenges.

Features - text relevance, customer reviews, purchase history, click-through rate, conversion rate, price, shipping. Use learning-to-rank framework (XGBoost, LambdaMART). Discuss personalization, query understanding, and balancing relevance with business metrics.

Break down calculation - daily visitors, current CTR, average order value, conversion rate. Show structured thinking with clear assumptions. Discuss sensitivity analysis and how to validate estimate. Connect to A/B testing and measurement strategy.

Calculate E[max(X,Y)] by summing over all possible maximum values weighted by their probabilities. For each value k from 1 to 6, P(max = k) = P(both ≤ k) - P(both ≤ k-1) = (k/6)^2 - ((k-1)/6)^2. The answer is 161/36 ≈ 4.47. Show the systematic calculation clearly.

The probability of 5 heads in a row is (1/2)^5 = 1/32. Fair value is $100 * 1/32 = $3.125. But as a trader, you would bid below fair value and offer above. Discuss how you would set bid-ask spread based on edge requirements and risk.

Use the difference of squares: 37 * 43 = (40-3)(40+3) = 1600 - 9 = 1591. Jane Street expects rapid mental math. Practice techniques like difference of squares, breaking into components, and estimation for quick verification.

Use Bayes' theorem. P(double-headed | 10 heads) = P(10H | double) * P(double) / P(10H). P(10H) = 1 * (1/100) + (1/1024) * (99/100). Work through the calculation carefully. The answer is 1024/1123 ≈ 91.2%. Show your Bayesian reasoning step by step.

Think about adverse selection and the winner's curse. Your expected profit depends on when your bid gets hit versus when your ask gets lifted. A naive midpoint quote will lose money because you disproportionately trade when your estimate is wrong. Discuss how to widen spreads to account for adverse selection.

Apply the Kelly Criterion. Optimal fraction = (bp - q) / b where b=1, p=0.6, q=0.4. Kelly fraction = (1*0.6 - 0.4)/1 = 0.2 or 20% of bankroll per bet. Discuss why maximizing expected value is different from maximizing expected log wealth and the practical considerations of Kelly sizing.

Jane Street values intellectual honesty deeply. Choose a genuine example of being wrong, how you recognized it, and how you updated your thinking. Show that you are comfortable with being wrong and can change your mind when presented with evidence.

Structure your estimate: Chicago population (~2.7M), households (~1M), piano ownership rate (~5%), tuning frequency (1-2x per year), pianos per tuner per day, working days per year. Show clear assumptions and arithmetic. Jane Street cares more about your structured approach than the exact number.

Be authentic about what draws you to Jane Street — the intellectual culture, collaborative environment, problem-solving nature of trading, or specific aspects of market-making. Show you understand what Jane Street does and why it appeals to you beyond compensation.

Expected value per bet = 0.5 * 1.5 - 0.5 * 1 = 0.25 (positive). You should play. For bet sizing, apply Kelly: f* = (0.5 * 1.5 - 0.5) / 1.5 = 1/3 of bankroll. Discuss the difference between a positive-EV game and optimal sizing, and why overbetting can still lead to ruin.